1. Technical Field
This invention relates to electric motors, and more particularly to an improved design for rotary brushless DC, stepping, and synchronous inductor motors which reduces a given harmonic of the fundamental (torque)/(displacement angle of the rotor) relationship.
2. Background Art
Rotary brushless DC, stepping, and synchronous inductor motors are well known in the art. Each type includes a rotor and a stator, with the stator having a plurality of salient poles energized by the passage of electric current through coils wound upon the poles. The coils are so arranged as to provide at least two electrical phases. The rotor includes at least one pair of N-S magnetic poles which are flux-linked with the stator poles, so that successive energizations of the phases provide rotary motion of the rotor.
The (torque)/(displacement angle of the rotor) relationship, "torque/angle curve", between a rotor pole and each of the stator poles, may be expressed in general by the well known Fourier expansion: EQU T=k [1+A.sub.1 cos.theta..sub.e +A.sub.2 cos2.theta..sub.e. . . A.sub.n cos.theta..sub.e +B.sub.1 sin.theta..sub.e +B.sub.2 sin
where
T=torque, PA1 k=a constant, PA1 A.sub.1, A.sub.2 . . . An=Fourier Coefficients (constants) of the cosine terms PA1 B.sub.1, B.sub.2 . . . Bn=Fourier Coefficients (constants) of the sine terms PA1 .theta..sub.e =the displacement of the rotor in electrical degrees.
In the equation, A.sub.1 cos.theta..sub.e +B.sub.1 sin.theta..sub.e represents the fundamental (first) harmonic produced as the rotor poles pass the stator poles; A.sub.2 cos2.theta..sub.e +B.sub.2 sin2.theta..sub.e is the second harmonic of the fundamental; and so forth.
In the special case in which .theta. is defined as the rotor position for which the centerline of the rotor pole coincides with the centerline of the stator pole for which the Fourier expansion is being written, the expansion is greatly simplified to
It is well known that the presence of torque/angle harmonics is especially detrimental to the performance of synchronous inductor motors, step motors, and brushless D.C. motors. In particular, a harmonic of the order corresponding to twice the number of phases (e.g. 4th harmonic for a 2-phase machine, 6th harmonic for a 3-phase machine, etc.) is particularly detrimental because of its dominance in the distribution of harmonic content. This particular harmonic is responsible for "detent torque", an objectionable resistance to rotation of the rotor of a de-energized motor. Step accuracy of a step motor, velocity modulation of synchronous inductor motors, step motors, and brushless D.C. motors, and microstepping ability of step motors and brushless D.C. motors are all adversely affected by torque/angle harmonics, and particularly by the one responsible for detent torque as described above.
It would be advantageous in such motors to be able to minimize the dominant harmonic which adversely affects motor performance as described above.
In U.S. Pat. No. 4,516,048, assigned to the assignee of the present application, there is disclosed means for minimizing a given harmonic of the torque/angle curve of motors by providing a stator with toothed poles, the teeth on the poles being set at a nonuniform pitch according to a specified relationship. While that arrangement satisfactorily reduces the harmonic, the stator poles of synchronous inductor motors, step motors, and brushless D.C. motors having a large angle of incremental motion, are commonly untoothed, precluding the use of the teaching embodied in U.S. Pat. No. 4,516,048.